Vol 11 Iss. 3

In a previous work devoted to the theory of a cylindrical ball mill, I studied the initial period of unsteady motion of the balls. If the angular velocity of rotation of the drum remains constant, then the regime of the ball mill after some time can be considered steady, and the magnitude and direction of the velocity of different balls passing through one and the same point in space do not change over time. We will talk about the outer row of balls. The same reasoning applies to other rows, if we make the assumption that the relative motion of the different rows is independent. This assumption, of course, requires additional research. The ball mill theory, which is usually used in practice, is approximate. The subject of this work is to refine the usual approximate theory of a ball mill.

The problem is to study the motion of a particle moving under the influence of gravity and in the presence of friction along the outer surface of a circular cylinder rotating around a horizontal axis. The problem under consideration finds application in some aspects of mineral processing, namely in the theory of a drum separator, used for ore enrichment, as well as in the theory of a drum dumper, which is intended to unload material moved by a belt conveyor at a certain point. The results obtained make it possible to clarify the above theories, which are usually presented in technical manuals.

One of the questions of the theory of screens and conveyors consists in the study of the motion, with friction, of the particles of some material on a surface which also performs a certain movement, the latter being indicated beforehand. For this purpose, one has to form differential equations concerning the motions of materials in the most general case of the movement of the screen and then to apply them to the case of plane motion, which is of practical importance. Lastly, there are indicated some particular cases of integrability of the differential equation obtained.

In this paper is examined a general case of the small vibrations of the inertial screen considered as a rigid body possessing all the 6 degrees of liberty. There are also determined the conditions under which the problem can be reduced to three degrees of liberty (the case examined in a previous paper entitled "Upon inertial screens"). Euler’s equations determining the motion of a rigid body are simplified considering the smallness of its vibrations and in the first approximation the problem is reduced to the solution of a system of 6 simultaneous linear equations with constant coefficients, or even to separate linear equations. In case of need the result can be improved by consecutive approximations taking also non-linear equations into consideration.

Starting a synchronous motor may be performed both with full voltage and lowered voltage. Fig. 1 shows a principal scheme of connecting a synchronous motor whose starting is performed under full voltage; principal schemes of connecting synchronous motors whose starting is performed under lowered voltage are represented in Fig. 2 and 3, respectively for cases of starting by means of a reactor and autotransformer. The present paper examines automatic control operations in compressor plants driven by synchronous motors whose starting is performed under full voltage; automatic protection of these plants from treating troubles is also considered. A method of starting synchronous motors under full voltage being the simplest both in its operations and with regard to its starting equipment is likely to be extensively adopted in next future in the mines of USSR where stations and substations under certain conditions of their capacity will admit of directly connecting powerful compressor plants served by synchronous motors.

As is known, a completely accurate determination of the individual parameters of a three-period tachogram of mine hoisting occurs when the tachogram is a trapezoid with straight sides. Below are proposed precise methods for determining the tachogram elements for two hoisting systems, given straight sides for the acceleration period t1 and corresponding curved sides for the deceleration period t2. Precise determination of the individual elements of the three-period tachogram is possible: 1) when its sides corresponding to the acceleration and deceleration periods are straight; 2) when one side corresponding to the acceleration period is straight and the other side corresponding to the deceleration period is curved according to a sine or hyperbolic sine law, provided that the acceleration period t1 is the unknown quantity. In the article are proposed exact methods for determining the elements of the tachogram for the two hoisting systems mentioned above, given the presence of straight-line segments for the starting period t1 and corresponding curved segments for the deceleration period t2. In practice, such tachograms can be used as design ones for the case of an asynchronous hoist motor, with contactor control employing appropriately adjusted time relays.

This article solves the problem of determining the smallest and largest resistances measurable on a bridge with a given accuracy, given the specified current sensitivity limit of the galvanometer and its internal resistance, under the following conditions: with a given electromotive force of the battery and its internal resistance; with a given current flowing through the unknown resistance; with a given power dissipated across the unknown resistance; with a given power consumed by the entire bridge. The first case is the most complex. It is considered only for the Wheatstone bridge. Furthermore, the article shows that when measuring small resistances, both bridges — Thomson and Wheatstone — can be used with equal success.

The conclusions can be characterized as follows: The values of the amplitudes of the diurnal variations of the magnetic field for the vertical component decrease with the diminution of the latitude of the place of observation. This regularity is observed in the middle latitudes of the USSR. Considering the insignificant magnitude of the maximum amplitudes of the diurnal variations of the vertical component of the magnetic field, it is possible not to introduce any corrections for variations in the case of measurement of the vertical component of the magnetic field in the middle latitudes (from 42° to 54° N. L.) of the USSR, if we can confine ourselves to an approximation of ±20 gammes in the results of measurements and verifications. In latitude higher than 54° N it is necessary to take into account the diurnal variations of the magnetic field if we wish to obtain results of measurements and verifications with a precision not under ±40 gammes for the vertical intensity. In cases of measurements of the horizontal intensity it is necessary to introduce corrections depending on variations in observations in every part of the USSR, if we desire to obtain results of measurements and verifications with a precision not under ±40 gammes.